Many-Body Derivations
Many-body derivations translate tensor-product quantum mechanics into occupation-number and field-operator language. The sign, normalization, and ordering conventions matter.
Identical Particles and Fock Space
Section titled “Identical Particles and Fock Space”- Symmetrization Postulate
- Pauli Exclusion Principle
- Occupation-Number Basis
- Bosonic Fock Space
- Fermionic Fock Space
Second Quantization
Section titled “Second Quantization”- Creation and Annihilation Operators
- Bosonic Commutation Relations
- Fermionic Anticommutation Relations
- Field Operators
- Mode Expansions
Operators and Correlations
Section titled “Operators and Correlations”- One-Body Operators
- Two-Body Operators
- Many-Particle Hamiltonians
- Number Operators
- Wick’s Theorem Preview
- Correlation Functions Formula Card
Statistical and Model Links
Section titled “Statistical and Model Links”- Ideal Fermi Gas
- Ideal Bose Gas
- Fermi-Dirac Distribution
- Bose-Einstein Distribution
- Density of States: First Encounter
References
Section titled “References”- A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems, Dover, 2003.
- G. D. Mahan, Many-Particle Physics, 3rd ed., Springer, 2000.
- P. Coleman, Introduction to Many-Body Physics, Cambridge University Press, 2015.